Quantum search in a nonclassical database of trapped ions
I. E. Linington, Peter A. Ivanov, Nikolay V. Vitanov · Physical Review A · 2009
We propose an implementation of the Grover's search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions $N$. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with $N$ ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.